By all accounts this band, who actually formed before I was even born, should be sitting squarely at the top along with the Beatles on this list.
For me it boils down to that damn stranded on a desert island thing. If it were named "The Rock Island" then possibly yes to it being The Stones, but for my handful of CD's to grab, I would always grab for the harder Zeppelin, Sabbath, and Purple for "The Hard Rock Island". Besides, I believe The Rock Island belongs to a railroad anyway! In either case, you know I would at least grab a "Sticky Fingers" along for the ride... (Read my full Rolling Stones review HERE!)